Codebook for useful class4im variables

• 894 subjects in Cleveland-Elyria with bmi and no history of diabetes (missing values singly imputed: assume MAR)
• There are 9 variables in the data but we’ll use only these five today.

• All subjects have hx_diabetes (all 0), and MMSA (Cleveland-Elyria).
• See Course Notes Chapter on BRFSS SMART data for variable details
• Appendix provides details on data development.

Data Load

class4im <- read_rds("c04/data/class4im.Rds")
class4im |> n_miss()

[1] 0

identical(nrow(class4im), n_distinct(class4im$ID))

[1] TRUE

Splitting the Sample

set.seed(432)    ## for future replication
class4im_split <- initial_split(class4im, prop = 3/4)
train_c4im <- training(class4im_split)
test_c4im <- testing(class4im_split)
c(nrow(class4im), nrow(train_c4im), nrow(test_c4im))

[1] 894 670 224

Models We’ll Build Today

1. Predict bmi using exer_any and genhealth (both categorical)

• without and then with an interaction between the two predictors

2. Add in a quantitative covariate, fruit_day, first simply as a main (and linear) effect
3. Incorporate the fruit_day information using a quadratic polynomial instead.
4. Incorporate the fruit_day information using a restricted cubic spline with 4 knots instead.

We’ll fit all of these models with lm, and assess them in terms of in-sample (training) fit and out-of-sample (testing) performance.

We could, but won’t transform our outcome.

bmi means by exerany and health

summaries_1 <- train_c4im |>
    group_by(exerany, health) |>
    summarise(n = n(), mean = mean(bmi), stdev = sd(bmi))
summaries_1 |> kable(digits = 2)

Code for Interaction Plot

ggplot(summaries_1, aes(x = health, y = mean, 
                        col = factor(exerany))) +
  geom_point(size = 2) +
  geom_line(aes(group = factor(exerany))) +
  scale_color_viridis_d(option = "C", end = 0.5) +
  labs(title = "Observed Means of BMI",
       subtitle = "by Exercise and Overall Health")

• Note the use of factor here since the exerany variable is in fact numeric, although it only takes the values 1 and 0.
  • Sometimes it’s helpful to treat 1/0 as a factor, and sometimes not.
• Where is the evidence of serious non-parallelism (if any) in the plot on the next slide that results from this code?

Resulting Interaction Plot

Building a Model (m_1) without interaction

m_1 <- lm(bmi ~ exerany + health,
          data = train_c4im)

• How well does this model fit the training data?

glance(m_1) |> 
    select(r.squared, adj.r.squared, sigma, nobs, 
           df, df.residual, AIC, BIC) |>
    kable(digits = c(3, 3, 2, 0, 0, 0, 1, 1))

Tidied ANOVA for m_1

tidy(anova(m_1)) |>
    kable(dig = c(0, 0, 2, 2, 2, 3))

Tidied summary of m_1 coefficients

tidy(m_1, conf.int = TRUE, conf.level = 0.90) |>
    kable(digits = c(0,2,2,2,3,2,2))

Interpreting m_1

• Effect of exerany?
• Effect of health = Fair instead of Excellent?

m_1 Residual Plots (conclusions?)

Adding the interaction term to m_1

m_1int <- lm(bmi ~ exerany * health,
             data = train_c4im)

• How does this model compare in terms of fit to the training data?

bind_rows(glance(m_1), glance(m_1int)) |> 
    mutate(mod = c("m_1", "m_1int")) |>
    select(mod, r.sq = r.squared, adj.r.sq = adj.r.squared, 
       sigma, nobs, df, df.res = df.residual, AIC, BIC) |>
    kable(digits = c(0, 3, 3, 2, 0, 0, 0, 1, 1))

ANOVA for the m_1int model

tidy(anova(m_1int)) |>
    kable(dig = c(0, 0, 2, 2, 2, 3))

ANOVA test comparing m_1 to m_1int

anova(m_1, m_1int)

Analysis of Variance Table

Model 1: bmi ~ exerany + health
Model 2: bmi ~ exerany * health
  Res.Df   RSS Df Sum of Sq      F    Pr(>F)    
1    664 24830                                  
2    660 23811  4    1019.6 7.0656 1.424e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Tidied summary of m_1int coefficients

tidy(m_1int, conf.int = TRUE, conf.level = 0.90) |>
    rename(se = std.error, t = statistic, p = p.value) |>
    kable(digits = c(0,2,2,2,3,2,2))

Interpreting the m_1int model

• How do we interpret effect sizes here? It depends.
• Effect of exerany?
  • If health = Excellent, effect is -1.69
  • If health = Fair, effect is (-1.69 - 6.22) = -7.91
• Effect of health = Fair instead of Excellent?
  • If exerany = 0 (no), effect is 7.64
  • If exerany = 1 (yes), effect is (7.64 - 6.22) = 1.42

Plot the Residuals from model m_1int?

Adding in the covariate fruit_day to m_1

m_2 <- lm(bmi ~ fruit_day + exerany + health,
          data = train_c4im)

• How well does this model fit the training data?

bind_rows(glance(m_1), glance(m_2)) |>
    mutate(mod = c("m_1", "m_2")) |>
    select(mod, r.sq = r.squared, adj.r.sq = adj.r.squared, 
        sigma, df, df.res = df.residual, AIC, BIC) |>
    kable(digits = c(0, 3, 3, 2, 0, 0, 1, 1))

ANOVA for the m_2 model

tidy(anova(m_2)) |>
    kable(dig = c(0, 0, 2, 2, 2, 3))

Tidied summary of m_2 coefficients

tidy(m_2, conf.int = TRUE, conf.level = 0.90) |>
    kable(digits = c(0,2,2,2,3,2,2))

m_2 Residual Plots (non-constant variance?)

Who is that poorest fit case?

Plot suggests we look at row 28

train_c4im |> slice(28) |>
    select(ID, bmi, fruit_day, exerany, health) |> kable()

What is unusual about this subject?

train_c4im |> arrange(desc(bmi)) 

# A tibble: 670 × 9
   ID      bmi inc_imp fruit_day drinks_wk female exerany health race_eth       
   <chr> <dbl>   <dbl>     <dbl>     <dbl>  <int>   <int> <fct>  <fct>          
 1 320    63     20581      1         0.7       1       0 P      Black non-Hisp…
 2 959    59.0    5720      0.1       0         1       0 F      White non-Hisp…
 3 1078   56.3   43948      1.02      0         1       0 F      White non-Hisp…
 4 633    51.5   39964      1         0         0       0 G      White non-Hisp…
 5 947    51.2   10280      2.02      0.93      1       0 F      White non-Hisp…
 6 535    50.5   22307      0.46      0         0       1 G      Hispanic       
 7 888    50.0  113725      2.02      0         1       1 G      White non-Hisp…
 8 743    49.0   31469      0.13      0         0       0 G      Black non-Hisp…
 9 551    48.8   91510      1.14      0.93      0       1 G      White non-Hisp…
10 924    48.2   11825      2         0         1       1 P      Multiracial no…
# ℹ 660 more rows

What if we included the interaction term?

m_2int <- lm(bmi ~ fruit_day + exerany * health, 
          data = train_c4im)

ANOVA for the m_2int model

tidy(anova(m_2int)) |>
    kable(dig = c(0, 0, 2, 2, 2, 3))

Tidied summary of m_2int coefficients

tidy(m_2int, conf.int = TRUE, conf.level = 0.90) |>
    rename(se = std.error, t = statistic, p = p.value) |>
    kable(digits = c(0,2,2,2,3,2,2))

ANOVA comparison of m_2 and m_2int

anova(m_2, m_2int)

Analysis of Variance Table

Model 1: bmi ~ fruit_day + exerany + health
Model 2: bmi ~ fruit_day + exerany * health
  Res.Df   RSS Df Sum of Sq      F    Pr(>F)    
1    663 24585                                  
2    659 23506  4    1079.2 7.5641 5.829e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual plots for model m_2int?

Which of the four models fits best?

In the training sample, we have…

• Adjusted \(R^2\), \(\sigma\), AIC and BIC all improve as we move down from m1 towards m2_int.
• BUT the training sample cannot judge between models accurately. Our models have already seen that data.
• For fairer comparisons, we’ll need to also consider the (held out) testing sample.

Model predictions of bmi in the test sample

We’ll use augment from the broom package…

m1_test_aug <- augment(m_1, newdata = test_c4im)
m1int_test_aug <- augment(m_1int, newdata = test_c4im)
m2_test_aug <- augment(m_2, newdata = test_c4im)
m2int_test_aug <- augment(m_2int, newdata = test_c4im)

This adds fitted values (predictions) and residuals (errors) …

m1_test_aug |> select(ID, bmi, .fitted, .resid) |> 
    slice(1:2) |> kable()

What does the yardstick package do?

For each subject in the testing set, we will need:

• estimate = model’s prediction of that subject’s bmi
• truth = the bmi value observed for that subject

Calculate a summary of the predictions across the \(n\) test subjects, such as:

• \(R^2\) = square of the correlation between truth and estimate
• mae = mean absolute error …

\[ mae = \frac{1}{n} \sum{|truth - estimate|} \]

• rmse = root mean squared error …

\[ rmse = \sqrt{\frac{1}{n} \sum{(truth - estimate)^2}} \]

Testing Results (using \(R^2\))

We can use the yardstick package and its rsq() function.

testing_r2 <- bind_rows(
    rsq(m1_test_aug, truth = bmi, estimate = .fitted),
    rsq(m1int_test_aug, truth = bmi, estimate = .fitted),
    rsq(m2_test_aug, truth = bmi, estimate = .fitted),
    rsq(m2int_test_aug, truth = bmi, estimate = .fitted)) |>
    mutate(model = c("m_1", "m_1int", "m_2", "m_2int"))
testing_r2 |> kable(dig = 4)

Mean Absolute Error?

Consider the mean absolute prediction error …

testing_mae <- bind_rows(
    mae(m1_test_aug, truth = bmi, estimate = .fitted),
    mae(m1int_test_aug, truth = bmi, estimate = .fitted),
    mae(m2_test_aug, truth = bmi, estimate = .fitted),
    mae(m2int_test_aug, truth = bmi, estimate = .fitted)) |>
    mutate(model = c("m_1", "m_1int", "m_2", "m_2int"))
testing_mae |> kable(dig = 2)

Root Mean Squared Error?

How about the square root of the mean squared prediction error, or RMSE?

testing_rmse <- bind_rows(
   rmse(m1_test_aug, truth = bmi, estimate = .fitted),
   rmse(m1int_test_aug, truth = bmi, estimate = .fitted),
   rmse(m2_test_aug, truth = bmi, estimate = .fitted),
   rmse(m2int_test_aug, truth = bmi, estimate = .fitted)) |>
   mutate(model = c("m_1", "m_1int", "m_2", "m_2int"))
testing_rmse |> kable(digits = 3)

Other Summaries for Numerical Predictions

Within the yardstick package, there are several other summaries, including:

• rsq_trad() = defines \(R^2\) using sums of squares.
  • The rsq() measure we showed a few slides ago is a squared correlation coefficient and is guaranteed to fall in (0, 1).
• mape() = mean absolute percentage error
• mpe() = mean percentage error
• huber_loss() = Huber loss (often used in robust regression), which is less sensitive to outliers than rmse().
• ccc() = concordance correlation coefficient, which attempts to measure both consistency/correlation (like rsq()) and accuracy (like rmse()).

See the yardstick home page for more details.

Incorporating a non-linear term for fruit_day

Suppose we wanted to include a polynomial term for fruit_day:

lm(bmi ~ fruit_day, data = train_c4im)
lm(bmi ~ poly(fruit_day, 2), data = train_c4im)
lm(bmi ~ poly(fruit_day, 3), data = train_c4im)

Polynomial Regression

A polynomial in the variable x of degree D is a linear combination of the powers of x up to D.

For example:

• Linear: \(y = \beta_0 + \beta_1 x\)
• Quadratic: \(y = \beta_0 + \beta_1 x + \beta_2 x^2\)
• Cubic: \(y = \beta_0 + \beta_1 x + \beta_2 x^2 + \beta_3 x^3\)
• Quartic: \(y = \beta_0 + \beta_1 x + \beta_2 x^2 + \beta_3 x^3 + \beta_4 x^4\)
• Quintic: \(y = \beta_0 + \beta_1 x + \beta_2 x^2 + \beta_3 x^3 + \beta_4 x^4 + \beta_5 x^5\)

Fitting such a model creates a polynomial regression.

Raw Polynomials vs. Orthogonal Polynomials

Predict bmi using fruit_day with a polynomial of degree 2.

(temp1 <- lm(bmi ~ fruit_day + I(fruit_day^2), 
             data = train_c4im))

Call:
lm(formula = bmi ~ fruit_day + I(fruit_day^2), data = train_c4im)

Coefficients:
   (Intercept)       fruit_day  I(fruit_day^2)  
       29.5866         -1.2726          0.1052  

This uses raw polynomials. Predicted bmi for fruit_day = 2 is

bmi = 29.5925 - 1.2733 (fruit_day) + 0.1051 (fruit_day^2)
    = 29.5925 - 1.2733 (2) + 0.1051 (4) 
    = 27.466

Does the raw polynomial match our expectations?

temp1 <- lm(bmi ~ fruit_day + I(fruit_day^2), 
             data = train_c4im)

augment(temp1, newdata = tibble(fruit_day = 2)) |>
    kable(digits = 3)

and this matches our “by hand” calculation. But it turns out most regression models use orthogonal rather than raw polynomials…

Fitting an Orthogonal Polynomial

Predict bmi using fruit_day with an orthogonal polynomial of degree 2.

(temp2 <- lm(bmi ~ poly(fruit_day,2), data = train_c4im))

Call:
lm(formula = bmi ~ poly(fruit_day, 2), data = train_c4im)

Coefficients:
        (Intercept)  poly(fruit_day, 2)1  poly(fruit_day, 2)2  
             28.084              -21.613                8.011  

This looks very different from our previous version of the model.

• What happens when we make a prediction, though?

Prediction in the Orthogonal Polynomial Model

Remember that in our raw polynomial model, our “by hand” and “using R” calculations both concluded that the predicted bmi for a subject with fruit_day = 2 was 27.466.

Now, what happens with the orthogonal polynomial model temp2 we just fit?

augment(temp2, newdata = data.frame(fruit_day = 2)) |>
    kable(digits = 3)

• No change in the prediction.

Fits of raw vs orthogonal polynomials

• The two models are, in fact, identical.

Why do we use orthogonal polynomials?

• The main reason is to avoid having to include powers of our predictor that are highly collinear.
• Variance Inflation Factor assesses collinearity…

vif(temp1)        ## from rms package

     fruit_day I(fruit_day^2) 
      4.652178       4.652178 

• Orthogonal polynomial terms are uncorrelated with one another, easing the process of identifying which terms add value to our model.

vif(temp2)      

poly(fruit_day, 2)1 poly(fruit_day, 2)2 
                  1                   1 

Why orthogonal rather than raw polynomials?

The tradeoff is that the raw polynomial is a lot easier to explain in terms of a single equation in the simplest case.

Actually, we’ll usually avoid polynomials in our practical work, and instead use splines, which are more flexible and require less maintenance, but at the cost of pretty much requiring you to focus on visualizing their predictions rather than their equations.

Adding a Second Order Polynomial to our Models

m_3 <- lm(bmi ~ poly(fruit_day,2) + exerany + health,
          data = train_c4im)

• Comparison to other models without the interaction…

Tidied summary of m_3 coefficients

m_3 Residual Plots

Add in the interaction

m_3int <- lm(bmi ~ poly(fruit_day,2) + exerany * health,
          data = train_c4im)

• Comparison to other models with the interaction…

Tidied summary of m_3int coefficients

m_3int Residual Plots

How do models m_3 and m_3int do in testing?

m3_test_aug <- augment(m_3, newdata = test_c4im)
m3int_test_aug <- augment(m_3int, newdata = test_c4im)

testing_r2 <- bind_rows(
    rsq(m1_test_aug, truth = bmi, estimate = .fitted),
    rsq(m2_test_aug, truth = bmi, estimate = .fitted),
    rsq(m3_test_aug, truth = bmi, estimate = .fitted),
    rsq(m1int_test_aug, truth = bmi, estimate = .fitted),
    rsq(m2int_test_aug, truth = bmi, estimate = .fitted),
    rsq(m3int_test_aug, truth = bmi, estimate = .fitted)) |>
    mutate(model = c("m_1", "m_2", "m_3", "m_1int",
                     "m_2int", "m_3int"))

• I’ve hidden my calculations for RMSE and MAE here.

Results comparing all six models (testing)

bind_cols(testing_r2 |> select(model, rsquare = .estimate), 
          testing_rmse |> select(rmse = .estimate),
          testing_mae |> select(mae = .estimate)) |>
    kable(digits = c(0, 4, 3, 3))

• Did the polynomial term in m_3 and m_3int improve our predictions?

Splines

• A linear spline is a continuous function formed by connecting points (called knots of the spline) by line segments.
• A restricted cubic spline is a way to build highly complicated curves into a regression equation in a fairly easily structured way.
• A restricted cubic spline is a series of polynomial functions joined together at the knots.
  • Such a spline gives us a way to flexibly account for non-linearity without over-fitting the model.
  • Restricted cubic splines can fit many different types of non-linearities.
  • Specifying the number of knots is all you need to do in R to get a reasonable result from a restricted cubic spline.

The most common choices are 3, 4, or 5 knots.

• 3 Knots, 2 degrees of freedom, allows the curve to “bend” once.
• 4 Knots, 3 degrees of freedom, lets the curve “bend” twice.
• 5 Knots, 4 degrees of freedom, lets the curve “bend” three times.

A simulated data set

set.seed(4322021)

sim_data <- tibble(
    x = runif(250, min = 10, max = 50),
    y = 3*(x-30) - 0.3*(x-30)^2 + 0.05*(x-30)^3 + 
        rnorm(250, mean = 500, sd = 70)
)

head(sim_data, 2)

# A tibble: 2 × 2
      x     y
  <dbl> <dbl>
1  42.5  397.
2  35.9  414.

The sim_data, plotted.

Fitting Restricted Cubic Splines with lm and rcs

sim_linear <- lm(y ~ x, data = sim_data)
sim_poly2  <- lm(y ~ poly(x, 2), data = sim_data)
sim_poly3  <- lm(y ~ poly(x, 3), data = sim_data)
sim_rcs3   <- lm(y ~ rcs(x, 3), data = sim_data)
sim_rcs4   <- lm(y ~ rcs(x, 4), data = sim_data)
sim_rcs5   <- lm(y ~ rcs(x, 5), data = sim_data)

Looking at the Polynomial Fits

Looking at the Restricted Cubic Spline Fits

Fitting Restricted Cubic Splines with lm and rcs

For most applications, three to five knots strike a nice balance between complicating the model needlessly and fitting data pleasingly. Let’s consider a restricted cubic spline model for bmi based on fruit_day again, but now with:

• in temp3, 3 knots, and
• in temp4, 4 knots,

temp3 <- lm(bmi ~ rcs(fruit_day, 3), data = train_c4im)
temp4 <- lm(bmi ~ rcs(fruit_day, 4), data = train_c4im)

Spline models for bmi and fruit_day

Let’s try an RCS with 4 knots

m_4 <- lm(bmi ~ rcs(fruit_day, 4) + exerany + health,
          data = train_c4im)

m_4int <- lm(bmi ~ rcs(fruit_day, 4) + exerany * health,
          data = train_c4im)

Comparing 4 models including the exerany*health interaction…

Tidied summary of m_4int coefficients

m_4int Residual Plots

How do models m_4 and m_4int do in testing?

I’ll note that there’s a fair amount of very repetitive code in the Quarto file to create that table.

• What are our conclusions?

Next Week

• Using the ols function from the rms package to fit linear regression models with non-linear terms.
• Be sure to submit Lab 2 to Canvas by Tuesday 2024-01-30 at Noon.

Creating Today’s Data Set

url1 <- "https://raw.githubusercontent.com/THOMASELOVE/432-data/master/data/smart_ohio.csv"

smart_ohio <- read_csv(url1)

class4 <- smart_ohio |>
    filter(hx_diabetes == 0, 
           mmsa == "Cleveland-Elyria",
           complete.cases(bmi)) |>
    select(bmi, inc_imp, fruit_day, drinks_wk, 
           female, exerany, genhealth, race_eth, 
           hx_diabetes, mmsa, SEQNO) |>            
    type.convert(as.is = FALSE) |>                       
    mutate(ID = as.character(SEQNO - 2017000000)) |>
    relocate(ID)

Codebook for useful class4 variables

• 894 subjects in Cleveland-Elyria with bmi and no history of diabetes

• plus ID, SEQNO, hx_diabetes (all 0), MMSA (all Cleveland-Elyria)
• See Course Notes Chapter on BRFSS SMART data for variable details

Basic Data Summaries

Available approaches include:

• summary
• mosaic package’s inspect()
• Hmisc package’s describe

all of which can work nicely in an HTML presentation, but none of them fit well on one of these slides.

Quick Histogram of each quantitative variable

Code for previous slide

p1 <- ggplot(class4, aes(x = bmi)) + 
    geom_histogram(fill = "navy", col = "white", bins = 20)
p2 <- ggplot(class4, aes(x = inc_imp)) + 
    geom_histogram(fill = "forestgreen", col = "white", 
                   bins = 20)
p3 <- ggplot(class4, aes(x = fruit_day)) + 
    geom_histogram(fill = "tomato", col = "white", bins = 20)
p4 <- ggplot(class4, aes(x = drinks_wk)) + 
    geom_histogram(fill = "royalblue", col = "white", 
                   bins = 20)
(p1 + p2) / (p3 + p4)

I also used #| warning: false in the plot’s code chunk label to avoid warnings about missing values, like this one for inc_imp:

Warning: Removed 120 rows containing non-finite values

Binary variables in raw class4

class4 |> tabyl(female, exerany) |> adorn_title()

        exerany        
 female       0   1 NA_
      0      95 268  20
      1     128 361  22

• female is based on biological sex (1 = female, 0 = male)
• exerany comes from a response to “During the past month, other than your regular job, did you participate in any physical activities or exercises such as running, calisthenics, golf, gardening, or walking for exercise?” (1 = yes, 0 = no, don’t know and refused = missing)

• Any signs of trouble here?
• I think the 1/0 values and names are OK choices.

Multicategorical genhealth in raw class4

class4 |> tabyl(genhealth)

   genhealth   n     percent valid_percent
 1_Excellent 148 0.165548098    0.16573348
  2_VeryGood 324 0.362416107    0.36282195
      3_Good 274 0.306487696    0.30683091
      4_Fair 112 0.125279642    0.12541993
      5_Poor  35 0.039149888    0.03919373
        <NA>   1 0.001118568            NA

• The variable is based on “Would you say that in general your health is …” using the five specified categories (Excellent -> Poor), numbered for convenience after data collection.
• Don’t know / not sure / refused were each treated as missing.
• How might we manage this variable?

Changing the levels for genhealth

class4 <- class4 |>
    mutate(health = 
               fct_recode(genhealth,
                          E = "1_Excellent",
                          VG = "2_VeryGood",
                          G = "3_Good",
                          F = "4_Fair",
                          P = "5_Poor"))

Might want to run a sanity check here, just to be sure…

Checking health vs. genhealth in class4

class4 |> tabyl(genhealth, health) |> adorn_title()

             health                   
   genhealth      E  VG   G   F  P NA_
 1_Excellent    148   0   0   0  0   0
  2_VeryGood      0 324   0   0  0   0
      3_Good      0   0 274   0  0   0
      4_Fair      0   0   0 112  0   0
      5_Poor      0   0   0   0 35   0
        <NA>      0   0   0   0  0   1

• OK. We’ve preserved the order and we have much shorter labels. Sometimes, that’s helpful.

Multicategorical race_eth in raw class4

class4 |> count(race_eth)

# A tibble: 6 × 2
  race_eth                     n
  <fct>                    <int>
1 Black non-Hispanic         167
2 Hispanic                    27
3 Multiracial non-Hispanic    19
4 Other race non-Hispanic     22
5 White non-Hispanic         646
6 <NA>                        13

“Don’t know”, “Not sure”, and “Refused” were treated as missing.

• What is this variable actually about?
• What is the most common thing people do here?

What is the question you are asking?

Collapsing race_eth levels might be rational for some questions.

• We have lots of data from two categories, but only two.
• Systemic racism affects people of color in different ways across these categories, but also within them.
• Is combining race and Hispanic/Latinx ethnicity helpful?

It’s hard to see the justice in collecting this information and not using it in as granular a form as possible, though this leaves some small sample sizes. There is no magic number for “too small a sample size.”

• Most people identified themselves in one of the categories.
• These data are not ordered, and (I’d argue) ordering them isn’t helpful.
• Regression models are easier to interpret, though, if the “baseline” category is a common one.

Resorting the factor for race_eth

Let’s sort all five levels, from most observations to least…

class4 <- class4 |>
    mutate(race_eth = fct_infreq(race_eth))

class4 |> tabyl(race_eth)

                 race_eth   n    percent valid_percent
       White non-Hispanic 646 0.72259508    0.73325766
       Black non-Hispanic 167 0.18680089    0.18955732
                 Hispanic  27 0.03020134    0.03064699
  Other race non-Hispanic  22 0.02460850    0.02497162
 Multiracial non-Hispanic  19 0.02125280    0.02156640
                     <NA>  13 0.01454139            NA

• Not a perfect solution, certainly, but we’ll try it out.

“Cleaned” Data and Missing Values

class4 <- class4 |>
    select(ID, bmi, inc_imp, fruit_day, drinks_wk, 
           female, exerany, health, race_eth, everything())

miss_var_summary(class4)

# A tibble: 13 × 3
   variable    n_miss pct_miss
   <chr>        <int>    <dbl>
 1 inc_imp        120   13.4  
 2 exerany         42    4.70 
 3 fruit_day       41    4.59 
 4 drinks_wk       39    4.36 
 5 race_eth        13    1.45 
 6 health           1    0.112
 7 genhealth        1    0.112
 8 ID               0    0    
 9 bmi              0    0    
10 female           0    0    
11 hx_diabetes      0    0    
12 mmsa             0    0    
13 SEQNO            0    0    

Single Imputation Approach?

set.seed(43203)
class4im <- class4 |>
    select(ID, bmi, inc_imp, fruit_day, drinks_wk, 
           female, exerany, health, race_eth) |>
    data.frame() |>
    impute_cart(health ~ bmi + female) |>
    impute_pmm(exerany ~ female + health + bmi) |>
    impute_rlm(inc_imp + drinks_wk + fruit_day ~ 
                   bmi + female + health + exerany) |>
    impute_cart(race_eth ~ health + inc_imp + bmi) |>
    tibble()

prop_miss_case(class4im)

[1] 0

Saving the tidied data

Let’s save both the unimputed and the imputed tidy data as R data sets.

write_rds(class4, "c04/data/class4.Rds")

write_rds(class4im, "c04/data/class4im.Rds")

To reload these files, we’ll use read_rds().

• The main advantage here is that we’ve saved the whole R object, including all characteristics that we’ve added since the original download.